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Computing regions of interest for geometric features in digital images

2009
*
Discrete Applied Mathematics
*

The focus is on the solution of

doi:10.1016/j.dam.2009.02.002
fatcat:evdgd3ajdradrmzbsdqkmwrtxy
*transformation*problems*for*geometric primitives, especially*lines*, so that regions of interest can be computed*for**corresponding*geometric features*in*distinct*images*. ... We present an uncertainty model*for*geometric*transformations*based on polygonal uncertainty regions and*transformation**polytopes*. ... Acknowledgments A preliminary version of this paper was presented at the 12th International Workshop on Combinatorial*Image*Analysis, Buffalo, NY, USA, April 2008 [9] . ...##
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Uncertain Geometry in Computer Vision
[chapter]

2005
*
Lecture Notes in Computer Science
*

We illustrate the use of uncertain geometry with examples involving the detection of circles and the computation of

doi:10.1007/978-3-540-31965-8_33
fatcat:ddqxvbilibdldmutwzfrlzmsgi
*transformations*between*images*. ... The statistical properties of these graphs are important when we design algorithms*for*the extraction of geometric primitives from*images*. ...*corresponding*feature point*in*the first*image*. ...##
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A generalized preimage for the digital analytical hyperplane recognition

2009
*
Discrete Applied Mathematics
*

Each point

doi:10.1016/j.dam.2008.05.030
fatcat:stl3ubrserh5bg32xae5irov6u
*in*this preimage*corresponds*to a Euclidean hyperplane the*digitization*of which contains all given hypervoxels. ... The principle is to incrementally compute*in*a dual space the generalized preimage of the ball set*corresponding*to a given hypervoxel set according to the chosen*digitization*model. ... Dual of a*polytope**In*order to define the dual of a*polytope*, we use a dual*transformation*similar to the well known Hough*transform*which is an efficient tool usually used*in**image*processing to recognize ...##
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Practical solutions for counting scalars and dependences in ATOMIUM-a memory management system for multidimensional signal processing

1997
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IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
*

Index Terms-Data dependence, data-flow analysis,

doi:10.1109/43.573828
fatcat:syi73xvvzfb6hehgsizkpbmtqm
*digital*signal processing (DSP), linearly bounded lattice,*polytope*. ... Therefore, the efficient handling of array references*in*the specifications*for**image*and video processing is crucial*for*obtaining low cost memory allocation solutions. ... As the*image**polytopes*can contain "holes," the equality of the*image**polytopes*is not a proof that the*corresponding*array references are equivalent. ...##
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On the recognition of digital circles in linear time

1993
*
Computational geometry
*

*For*a given object s E R" one can obtain the so-called

*digitalization*dig(s) of s. One problem of the

*image*processing is the recognition of objects s c R", where y = dig(s) is given. ... ., On the recognition of

*digital*circles

*in*linear time; Computational Geometry: Theory and Applications 2 (1993) 287-302. ...

*For*these reasons we firstly attempt to

*transform*

*digital*circles to

*digital*straight

*lines*and vice versa. ...

##
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Some theoretical challenges in digital geometry: A perspective

2009
*
Discrete Applied Mathematics
*

The explicit purpose of the present Perspective is to suggest a number of strategic objectives

doi:10.1016/j.dam.2009.04.022
fatcat:3nvxwk5u4zhqlagcydyknwejmq
*for*theoretical research, with an emphasis on the combinatorial approach*in**image*analysis. ...*In*recent years*image*analysis has become a research field of exceptional significance, due to its relevance to real life problems*in*important societal and governmental sectors, such as medicine, defense ... Acknowledgements The authors are obliged to the two anonymous referees*for*their useful remarks and suggestions. The authors thank Amy Cuhel-Schuckers and Boris Brimkov*for*proofreading the text. ...##
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Topological Superfluid Defects with Discrete Point Group Symmetries
[article]

2022
*
arXiv
*
pre-print

*In*this work we create and verify exotic magnetic phases of atomic spinor Bose-Einstein condensates that, despite their continuous character and intrinsic spatial isotropy, exhibit complex discrete

*polytope*... We show how filling the vortex

*line*singularities with atoms

*in*a variety of different phases leads to core structures that possess magnetic interfaces with rich combinations of discrete and continuous ... ACKNOWLEDGMENTS The authors are grateful

*for*experimental assistance from L. Reuter

*in*obtaining the data presented

*in*Fig. 5 ...

##
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Right-angled Coxeter polytopes, hyperbolic 6-manifolds, and a problem of Siegel
[article]

2010
*
arXiv
*
pre-print

By gluing together the sides of eight copies of an all-right angled hyperbolic 6-dimensional

arXiv:1009.3231v1
fatcat:skbajufafzb7ln3kodcceza25i
*polytope*, two orientable hyperbolic 6-manifolds with Euler characteristic -1 are constructed. ... The*images**in*(Z/2) 27 of the side-pairing*transformations*of Q are the 21 vectors v i = w i +e i ,*for*i = 7, . . . , 27, where w i is the base 2 vector representing the (i−6)th*digit*of the code*for*... of Γ n 2 of order 2 n−1 ,*corresponding*to the l n*line*edges of P n*for*2 ≤ n ≤ 7. ...##
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Digital Analytical Geometry: How Do I Define a Digital Analytical Object?
[chapter]

2015
*
Lecture Notes in Computer Science
*

We will end with open problems and challenges

doi:10.1007/978-3-319-26145-4_1
fatcat:y44bugcgrvdmjp4ahfiij7vogm
*for*the future. ... We will then explain how, from simple assumptions about properties a*digital*object should have, one can build mathematical sound*digital*objects. ... I am not quite sure that there exists a*corresponding*3D plane thickness (and thus a*corresponding*general*digitization**transform*) that would dene such*digital*3D*lines*. ...##
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Linearly constrained Bayesian matrix factorization for blind source separation

2009
*
Neural Information Processing Systems
*

This

dblp:conf/nips/Schmidt09
fatcat:gsmfzm2rhfgpbhef74pxsgwg4e
*transformation*ensures, that*for*any value of y, the*corresponding*x satisfies the equality constraints. ... Task The objective is to factorize the data matrix*in*order to find a number of source*images*that explain the data. Ideally, the sources should*correspond*to the original*digits*. ... From these*images*we created 4, 000*image*mixtures by adding the grayscale intensities of the*images*two and two, such that the different*digits*were combined*in*equal proportion. ...##
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A Tutorial on Well-Composedness

2017
*
Journal of Mathematical Imaging and Vision
*

Believing

doi:10.1007/s10851-017-0769-6
fatcat:pwvvx5rvlndblkexm5tj6y4y7i
*in*its prime importance*in**digital*topology, we then propose this state-of-the-art of well-composedness, summarizing its different flavours, the different methods existing to produce well-composed ... To get rid of those paradoxes, and to restore some topological properties to the objects contained*in*the*image*, like manifoldness, Latecki proposed a new class of*images*, called wellcomposed*images*, with ... By construction, their connected components are respectively open sets*for*the miss-*transform*, and closed sets*for*the hit-*transform*. ...##
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Polytopic Planar Region Characterization of Rough Terrains for Legged Locomotion
[article]

2022
*
arXiv
*
pre-print

This problem is of great importance

arXiv:2207.03098v1
fatcat:n3pdlnesijhxdi3ewjdafbseoe
*for*terrain mapping*in*complicated environment and has great potentials*in*legged locomotion applications. ... At the first stage, the planar regions embedded within a sequence of depth*images*are extracted individually first and then merged to establish a terrain map containing only planar regions*in*a selected ... With labeled pixels*in*the camera space, a*digitized*binary*image*is obtained*for*each plane. We then extract the boundary of each plane*in*the camera space. ...##
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Combinatorial approach to image analysis

2009
*
Discrete Applied Mathematics
*

The focus is on the solution of

doi:10.1016/j.dam.2009.06.030
fatcat:skntxcwdybdvjgohod32jxvixi
*transformation*problems*for*geometric primitives, especially*lines*, so that regions of interest can be computed*for**corresponding*geometric features*in*distinct*images*. ...*In*the first one, Kristof Teelen and Peter Veelaert present an uncertainty model*for*geometric*transformations*based on polygonal uncertainty regions and*transformation**polytopes*. ...##
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Learning a Continuous Hidden Variable Model for Binary Data

1998
*
Neural Information Processing Systems
*

The advantages of this approach are illustrated on a translationally invariant binary distribution and on handwritten

dblp:conf/nips/LeeS98
fatcat:lx2nuf6e6fdazc3bcg5qzmzogi
*digit**images*. ... A directed generative model*for*binary data using a small number of hidden continuous units is investigated. ... Seung*for*helpful discussions. ...##
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Fast penetration depth computation for physically-based animation

2002
*
Proceedings of the 2002 ACM SIGGRAPH/Eurographics symposium on Computer animation - SCA '02
*

It uses bounding volume hierarchies, object-space and

doi:10.1145/545265.545266
fatcat:c43zcmxpz5fmlglstehufacr7y
*image*-space culling algorithms to further accelerate the computation and refines the estimated PD*in*a hierarchical manner. ... We demonstrate its application to contact response computation and a time-stepping method*for*dynamic simulation. ... Acknowledgments This research was supported*in*part by ARO Contract DAAG55-98-1-0322, DOE ASCII Grant, NSF NSG-9876914, NSF DMI-9900157, NSF IIS-982167, NSF ACR-0118743, ONR Contracts N00014-01-1-0067 ...
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